Tool/Simplifier of math expressions. Simplification is a mathematical process aiming to rewrite an expression with the minimal number of items and variables.
Math Expression Simplifier - dCode
Tag(s) : Symbolic Computation
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Math Expression Simplifier
Mathematical Expression Simplifier
Boolean Expression Simplifier
Answers to Questions (FAQ)
What is a simplification in mathematics? (Definition)
Simplifying a mathematical calculation refers to the act of transforming an expression into an equivalent, more compact, or easier-to-manipulate form without changing its meaning.
Simplifying means rewriting an expression (numerical or algebraic) to make it easier to read or use in subsequent calculations.
The expression to be rewritten/simplified can be algebraic/formal, containing letters and/or numbers.
How to simplify a math expression?
To simplify an algebraic expression, apply transformations that preserve equivalence, such as reducing fractions, factoring, using notable identities, removing opposite terms, or simplifying roots.
Example: Expression Simplification: $$ \frac{x^2-4}{\frac{(x-2) \left(x^2+4 x+4\right)}{x^2-x-6}} = x-3 $$
The dCode Simplifier can perform any operation to reduce the mathematical expression to a simplified form. If needed, it is possible to force factoring of an expression or to expand and reduce a formula using the dedicated tools.
How to simplify a formula with remarkable identities?
To simplify a formula with notable identities, identify the relevant identities for the given expression and then apply them.
The remarkable identities allow a factorization of the mathematical expression and thus a simplification of its writing.
Example: $ (x-1)(x+1) = x^2-1 $
How to simplify fractions to irreducible form?
dCode calculator create irreducible fractions (see gcd) and reduce them to the same denominator (see lcm).
Example: $ \frac{15}{8} - \frac{2}{3} = \frac{29}{24} $
How to simplify logarithms or exponentials?
To simplify expressions with exponentials or logarithms, use properties of exponentials or logarithms to combine/extract similar terms.
Example: $ a^m \cdot a^n = a^{m + n} $
Example: $ \log_a(bc) = \log_a(b) + \log_a(c) $
How to simplify trigonometric expressions?
Simplifying trigonometric expressions consists of using trigonometric identities, to transform the equation into a more manageable form.
Example: $ \sin^2(x) + \cos^2(x) = 1 $ or $ \sin(2a) = 2\sin(a)\cos(a) $
How to simplify radix (roots) expression?
To simplify a root, look for square factors in the radicand and then extract them from the root.
dCode simplifies writing with radicals (nth root). Square roots can be indicated with the sqrt() function.
Example: $ \sqrt{8}+\sqrt{2} = 3\sqrt{2} $
How to simplify a polynomial?
Simplifying a polynomial involves grouping terms of the same degree, ordering the monomials, and reducing the coefficients.
Example: $ 3x^2 - x + 5 + 2x^2 + 4x $ becomes $ 5x^2 + 3x + 5 $
Is a simplified expression always unique?
An expression can have several equivalent simplified forms.
Example: $ \frac{1}{\sqrt{2}} $ and $ \frac{\sqrt{2}}{2} $ are two acceptable simplified forms.
How to simplify a mathematical equation?
To simplify a mathematical equation, the user can perform simplification operations on both sides of the equation to maintain equivalence.
NB: Simplifying is not solving, solving an equation aims to find the values of the unknown variable which satisfy the equation.
Source code
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- Mathematical Expression Simplifier
- Boolean Expression Simplifier
- What is a simplification in mathematics? (Definition)
- How to simplify a math expression?
- How to simplify a formula with remarkable identities?
- How to simplify fractions to irreducible form?
- How to simplify logarithms or exponentials?
- How to simplify trigonometric expressions?
- How to simplify radix (roots) expression?
- How to simplify a polynomial?
- Is a simplified expression always unique?
- How to simplify a mathematical equation?
